Properties

Label 1216.3.j
Level $1216$
Weight $3$
Character orbit 1216.j
Rep. character $\chi_{1216}(113,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $156$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1216.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1216, [\chi])\).

Total New Old
Modular forms 656 164 492
Cusp forms 624 156 468
Eisenstein series 32 8 24

Trace form

\( 156 q - 4 q^{5} + O(q^{10}) \) \( 156 q - 4 q^{5} + 4 q^{11} - 8 q^{17} - 30 q^{19} - 192 q^{35} + 4 q^{43} + 132 q^{45} + 8 q^{47} - 932 q^{49} - 68 q^{61} - 384 q^{63} + 192 q^{77} - 1124 q^{81} - 156 q^{83} + 216 q^{85} + 32 q^{93} - 380 q^{95} - 484 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(1216, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)